Wahlund effect
Encyclopedia
In population genetics
, the Wahlund effect refers to reduction of heterozygosity in a population
caused by subpopulation structure. Namely, if two or more subpopulations have different allele frequencies
then the overall heterozygosity is reduced, even if the subpopulations themselves are in a Hardy-Weinberg equilibrium. The underlying causes of this population subdivision could be geographic barriers to gene flow followed by genetic drift
in the subpopulations.
The Wahlund effect was first documented by the Swedish geneticist Sten Wahlund in 1928.
, with allele frequencies of A and a given by 
and 
respectively (
). Suppose this population is split into two equally-sized subpopulations, 
and 
, and that all the A alleles are in subpopulation 
and all the a alleles are in subpopulation 
(this could easily occur due to drift). Then, there are no heterozygotes, even though the subpopulations are in a Hardy-Weinberg equilibrium.
and 
represent the allele frequencies of A in 
and 
respectively (and 
and 
likewise represent a).
Let the allele frequency in each population be different, i.e.
.
Suppose each population is in an internal Hardy-Weinberg equilibrium, so that the genotype frequencies
AA, Aa and aa are p2, 2pq, and q2 respectively for each population.
Then the heterozygosity (
) in the overall population is given by the mean
of the two:
which is always smaller than
( = 
) unless 
.
Population genetics
Population genetics is the study of allele frequency distribution and change under the influence of the four main evolutionary processes: natural selection, genetic drift, mutation and gene flow. It also takes into account the factors of recombination, population subdivision and population...
, the Wahlund effect refers to reduction of heterozygosity in a population
Population
A population is all the organisms that both belong to the same group or species and live in the same geographical area. The area that is used to define a sexual population is such that inter-breeding is possible between any pair within the area and more probable than cross-breeding with individuals...
caused by subpopulation structure. Namely, if two or more subpopulations have different allele frequencies
Allele frequency
Allele frequency or Gene frequency is the proportion of all copies of a gene that is made up of a particular gene variant . In other words, it is the number of copies of a particular allele divided by the number of copies of all alleles at the genetic place in a population. It can be expressed for...
then the overall heterozygosity is reduced, even if the subpopulations themselves are in a Hardy-Weinberg equilibrium. The underlying causes of this population subdivision could be geographic barriers to gene flow followed by genetic drift
Genetic drift
Genetic drift or allelic drift is the change in the frequency of a gene variant in a population due to random sampling.The alleles in the offspring are a sample of those in the parents, and chance has a role in determining whether a given individual survives and reproduces...
in the subpopulations.
The Wahlund effect was first documented by the Swedish geneticist Sten Wahlund in 1928.
Simplest example
Suppose there is a population, with allele frequencies of A and a given by and respectively (). Suppose this population is split into two equally-sized subpopulations, and , and that all the A alleles are in subpopulation and all the a alleles are in subpopulation (this could easily occur due to drift). Then, there are no heterozygotes, even though the subpopulations are in a Hardy-Weinberg equilibrium.Case of two alleles and two subpopulations
To make a slight generalization of the above example, let and represent the allele frequencies of A in and respectively (and and likewise represent a).Let the allele frequency in each population be different, i.e.
.Suppose each population is in an internal Hardy-Weinberg equilibrium, so that the genotype frequencies
Genotype frequency
In population genetics, the genotype frequency is the frequency or proportion In population genetics, the genotype frequency is the frequency or proportion In population genetics, the genotype frequency is the frequency or proportion (i.e. 0 In population genetics, the genotype frequency is the...
AA, Aa and aa are p2, 2pq, and q2 respectively for each population.
Then the heterozygosity (
) in the overall population is given by the meanMean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
of the two:
 |
 |
 |
|
 |
which is always smaller than
( = ) unless Generalization
The Wahlund effect may be generalized to different subpopulations of different sizes. The heterozygosity of the total population is then given by the mean of the heterozygosities of the subpopulations, weighted by the subpopulation size.- De Finetti diagramDe Finetti diagramA de Finetti diagram is a ternary plot used in population genetics. It is named after the Italian statistician Bruno de Finetti and is used to graph the genotype frequencies of populations, where there are two alleles and the population is diploid...
(see Li 1955)
F-statistics
The reduction in heterozgosity can be measured using F-statisticsF-statistics
In population genetics, F-statistics describe the level of heterozygosity in a population; more specifically the degree of a reduction in heterozygosity when compared to Hardy–Weinberg expectation...
.